UNIT-05
POSETS, HASSE DIAGRAM AND LATTICES
UNIT-05/ LECTURE -01
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 404-408}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Draw the Hasse diagram of D60 (divisors of 60) |
June 2004 |
10 |
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Q 2 |
Let A= {a, b,c,d} and P(A) its power set. Draw Hasse diagram of [ P(A), C] |
June 2008 |
7 |
ORDERED SUBSETS
UNIT -05/ LECTURE-02
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 404-408}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Consider the hasse diagram of Poset as shown in fig a4 a5
a1 (i) Determine the least and greatest element of Poset if they exist (ii)Determine L.U.B of all pair of elements (iii) Determine G.L.B of all pair of elements.
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Dec 2013 |
7 |
LATTICES
UNIT-05/ LECTURE- 03
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 418-419}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Write short note on Lattice |
June 2003, Dec 2003, June 2014 |
2 |
SUB LATTICES, TYPES OF LATTICES, PROPERTIES OF LATTICES
UNIT-05/ LECTURE-04
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 425-427}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Write short notes on the following (i) Complemented lattice (ii) Lattice Homeomorphism (iii) Sublattice |
June 2011 |
7 |
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Q 2 |
Let L= {1,2,3,4,6,8,9,12,18,24} be ordered by the relation ‘/’ where x/y means ‘ x divides y’. Show that D24 set of all divisors of the integer 24 of L is a sublattice of the lattice (L,/). |
Dec 2009, June 2011, June 2013 |
7 |
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Q.3 |
Let L be the set of all factors of 12 and ‘/’ be the divisibility relation on L. Show that (L,’/’) is a lattice. |
Dec 2012 |
7 |
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Q.4 |
Define the following (i) Distributive lattice (ii) Complemented lattice (iii) Bounded lattice |
Dec 2013 |
7 |
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Q. 5 |
Prove that in a distributive lattice if an element has a complement then this complement is unique |
June 2010, June 2012, June 2014 |
7,2 |
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Q.6 |
In a complemented Distributive lattice L prove that (a ^ b)’’= a’ v b’, a,b € L |
June 2014 |
3 |
RECURRENCE RELATION
UNIT- 05/ LECTURE -05
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 441-446}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Solve the recurrence relation ar -6ar-1 + 8ar-2 =0 given a0 =3, a1 =2 |
June 2011 |
7 |
PROBLEMS ON RECURRENCE RELATION
UNIT-05/ LECTURE- 06
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 447-453}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Solve the recurrence relation ar -7ar-1 + 10ar-2 =0 given a0 =0 and a1 =3 |
Dec 2008 |
7 |
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Q 2 |
Given that a0 =0 , a1 =1, a2 =4 and a3 =12 satisfy the recurrence relation ar +c1 ar-1 + c2 ar-2 =0 Determine ar |
Dec 2002,2003,2004 |
2 |
PARTICULAR SOLUTION
UNIT-05/ LECTURE- 07
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 453-460}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Determine the particular solution for the difference equation Ar – 2ar-1 = f(r) where f(r)=7r |
Dec 2007 June 2009 |
7 |
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Q 2 |
Solve ar +5ar-1 +6ar-2 = 3r2 -2r +1 |
Dec 2008 |
7 |
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Q.3 |
Solve the recurrence relation ar – 5ar-1 + 6ar-2 = r2 – r, r>=2 |
June 2014 |
7 |
PROBLEMS ON RECURRENCE RELATIONS
UNIT-05/ LECTURE-07
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 453-460}
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S.NO |
RGPV QUESTIONS |
Year |
Marks |
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Q.1 |
Solve the recurrence relation ar -5ar-1 +6ar-2 = 2r +r, r>=2 |
Dec 2013 |
7 |
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Q 2 |
Determine the particular solution for ar -4ar-1 +4ar-2 =2r |
June 2005 |
5 |
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Q.3 |
Solve the recurrence relation ar + 6ar-1 +9ar-2 =3 given that a0 =0 and a1=1 |
June 2007 June 2010 |
5 |
PERMUTATIONS, COMBINATIONS, BINOMIAL THEOREM
UNIT-05/ LECTURE-08
REFERENCES {DISCRETE STRUCTURES BY D C AGARWAL, 432-440}
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REFERENCE |
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BOOK |
AUTHOR |
PRIORITY |
|
Discrete Structures |
D C Agarwal |
1 |
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Discrete Structures |
C.L Liu |
2 |